SUPERDIFFUSIVITY IN FIRST-PASSAGE PERCOLATION

Authors
LICEA C NEWMAN CM PIZA MST
Citation
C. Licea et al., SUPERDIFFUSIVITY IN FIRST-PASSAGE PERCOLATION, Probability theory and related fields, 106(4), 1996, pp. 559-591
Citations number
22
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Probability theory and related fields → ACNP
ISSN journal
01788051
Volume
106
Issue
4
Year of publication
1996
Pages
559 - 591
Database
ISI
SICI code
0178-8051(1996)106:4<559:SIFP>2.0.ZU;2-N
Abstract
In standard first-passage percolation on Z(d) (with d greater than or equal to 2), the time-minimizing paths from a point to a plane at dist ance L are expected to have transverse fluctuations of order L(xi). It has been conjectured that xi(d) greater than or equal to 1/2 with the inequality strict (superdiffusivity) at least for low d and with xi(2 )= 2/3. We prove (versions of) xi(d) greater than or equal to 1/2 for all d and xi(2) greater than or equal to 3/5.